Function generator of two independent variables



Nov. 11, 1958 HENRIY-GEORGES DOLL 2,859,915

FUNCTION GENERATOR OF TWO INDEPENDENT VARIABLES Filed June 2. 1953 ELECTRONIC ELECTRONIC PULSE AMPLIFIER COUNTER FIGJ COUNTER n F. H m I W UI m rnfil h 1 WW2! m FIG.3

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INVENTOR. HE NRI,GEORGES DOLL BY HIS ATTORNEY United States Patent 2,859,915 FUNCTION GENERATOR OF TWO INDEPENDENT VARIABLES Henri-Georges Doll, Ridgeiield, Conm, assignor, by theme assignments, to Schlumberger Well Surveying Corporation, Houstor'n'Telxl, a corporation of Texas Application "June 2, 195 3, 'Srial'No.'359,19

12 Claims. (Cl. 235- 61) This invention relates to automatic computers and,

more particularly, pertains to "an improved computer of the type providinga signal continuously representative of the vallue of a specified'functio'n 'of a plurality of in-.

dependent variables, according to instantaneous values 0 the variables supplied thereto.

1 In the copending application of H. G. Doll, July 1, 1952, hearing the Serial Numberp296,675, there is disclosed one form of apparatus of the above-defined type. According to that disclosure, a predetermined functionof one variable x is plotted as a change in light transmission eoefiicient on a first movable track and a. predetermined function 'of a second variable y is plotted as a light transmission coe'fiicient change on a second track movable in synchronism with the first track. By scanning each track with a light beam, whose instantaneous position is a function of the instantaneous-value of one of the independent variables, and combining the modulated light output from the tracks, instantaneous solutions it to the desired function, Luy (x, y), are automatically obtained.

It is an object of the present invention to eflfect certain improvements in the apparatus described in the aforementioned Doll application.

Another object of the present invention is to provide a computer of the type in which two functions are plotted on a common track featuring greater compactness than heretofore possible. A further object of the present invention is to provide an improved computer of the type wherein two functions are plotted on a common track that is readily convertible from one function of independent variables to a different function. V

In brief, an automatic computing apparatusin accordance with the present invention comprises means for deriving a-pair of beams of radiant energy individually positionable in response to the value of one ofa pair of independent variables. A screen is mounted for movement along a path intercepting both beams and includes a plurality of sections'occu'rring in two groups, each representing a preselected function. of one of the aforesaid variables in terms of a modified effect on incident radiant energy. Thesections in thetwo groups are distributed along the path of movement of the screenin a predetermined alternating order relationship andmeans are provided for intercepting modified radiant energy and for deriving an output energy during operating intervals wherein the sections in one group intercept a selected beam and the sections in the other "group intercept the remaining beam. v I

The novel features of the present invention are set forth with particularity in the appended claims. The present invention, both as to its organization and manner of operation, together with further objects and advanrages thereof, may best be understood B'mjereren e to the following description taken in connection with the accompanying drawing in which; p o I Fig. l is a perspective view of an automatic com- 2 putenparts thereof being shownin blockyfo'rm, constructed in -accordance with the presentiinvention; 1

Fig. 2 isia'series of curves representing 'the time sequence of various signals derived in the apparatus'illustrated in Fig.1; and. J

Fig. 3 represents a modification of the computer shown in Fig, 1.

a In Fig. 1 of the drawingjthere is shown a circulardisc .1 0 constructed of a transparent material such as'g'lass.

On one segmental half-section 11.,ofdisc 10. .there is inscribed a family of curves 12 correspondingjtoatpredetermined function u of twoindependent.variablesfx and y; i.;e., u=f (x,:y) ,Curves 12 are opaque and may 'be formed in any known manner, for example, by the photo-deposition process.

Light energy from a lightsource1'3 is projected toward the face of disc 10 ,afterreflection. from "a mirrortype galvanometer14, A voltage having. a magnitude proportional to thevalue of one of the independent-variables, x for example, is supplied'to galv'anomet'e'r 14. Thus, the radial ,positionof light beam v15 on theudis'c is dependent upon the instantaneous value of. variable, x. Disc 10 is continuously rotatedv by a m'otor16 and beam 15 is affected or modulated by the family of curves 12 during each one-halfcycleof rotation in which the curves intercept the beam before it impinges upon an elongated photo-electriccell 17.. The photocell has a length substantially equal to onerhalf the diameter of disc 10, so that lightener gy in beam 15, strikes theactive element of the cell at any radial position of'the beam. It is thus apparent that vthe electricaloutput between conductors 18 extending from photocell '17 isdependerit upon the instantaneous value ,of independent. variable x; i, e., the time-spacing and/ or position of the output pulses at leads 18 are dependent upon variable 'x. .lllfthemodulated output wave is integrated withr'espect to time limits determined by the instantaneous :value of, a second 'independent variable y in other words, if the pulses-occurring during a time interval determined by variable yare counted, an instantaneous value of u is automatically attained.

To that end, light energy from another source, 1 .is

reflected by a secondmirrorgalvanometer 20 and projected as a beam 21 toward dis c 10. ,Beam ,-21 is disposed diametrically oposite beam 15, relative to the disc, and its radialposition pn the gdisc is determined by the potential applied to galvanorneter 20,. This potentialis dependent upon the instantaneous value of independent variable y. Plotted on the remaining half-segment 22 of disc 10 is an opaque region 23 which interrupts the light beam 21 as the disc rotates. This occurs during each rotation 'of disc section 22,past the light beam and the duration of each interruption is dependent upon the instantaneous value of ,variabley'. For example, the periods of interuption may be proportional to .the in stantaneous value of variable] y. After modulation, light beam 21 is intercepted by a second, elongated .photo electric cell 24 and electrical outputin the "form of rectangular pulses appears at its leads 25.

In {order to synchronize the operation of the sy'ste'rn just-described so that pulses are derived from light be 15 only for curve family 1'2, and those derived fromli'g'ht beam 21 are representative only of function 23, disc 19 is provided with a peripheral, arcuate, opaque strip 26 on the segmental one-half section '11', and '9. corresponding transparent strip 27 is provided 'on 'half-sectionf22. Light. energy from a source 28 is concentrated-byacon densing lens 29 on the path traversed by strips 26fand 27 and is intercepted by a pfiotoelectric'cell 30 whose output leads 31 are connected to the actuating portions (notshown) of each of a pair of conventional electronic switches 32 and 33. Leads 18 from cell 17 and leads from cell 24 are connected to the respective input circuits (not shown) of switches 32 and 33. The electronic switches are arranged so that in response to incident light of high intensity at photocell both switches are rendered inoperative, whereas, for light of low in tensity,"the switches are operatively conditioned.

Output signals from the electronic switches are supplied via leads 34 and via leads to a pulse amplifier 36 electrically coupled in cascade with a pulse counter 37 and an output device 38. I

The operation of the system just-described may be best understood by reference to Fig. 2, which represents various waveforms of the system, plotted to a common time scale. For convenience of explanation, it is assumed that the photocells produce positive output pulses 'in response to interruption of the associated light beam by the passage of an opaque portion of the'rotating disc.

Galvanometers 14 and 20 are supplied with signals having magnitudes dependent upon the instantaneous values of independent variables x and respectively, and

light beams 15 and 21 are displaced in accordance with these values, as shown by the arrows x and y in Fig.

.1 When the family of curves 12 sweeps past light beam 15, a plurality of pulses, such as those represented by the groups of short vertical lines in Fig. 2a, are derived. The time displacement between adjacent pulses in each of groups 40, of course, is dependent upon the instantaneous value of variable x and the speed of rotation of disc 10.

At the same instant, light energy of beam 21 ir'npings upon section 22 of the rotating disc .at a radial position determined by the instantaneous value of variable y. .As the disc section 22 carrying function 23 sweeps past beam 21, a rectangular pulse of waveform 41 (Fig. 2b) is generated. The duration of each of pulses 41 is determined by the value of variable y and the rotational speed of disc 10. By maintaining the rotational speed constant and providing a suitable configuration for function 23, the duration of each of pulses 41 may be proportional to the instantaneous amplitude value of variable y.

Of course, as shown in Fig. 211, there are generated between pulse groups 40 rectangular pulses 42 which represent the modulation of light beam 15 byfunction 23. Similarly, as shown in Fig. 2b, the rectangular pulses 41 are interspersed with pulsegroups 43 caused by modulation of light beam 21 during its interception by curve family 12. I

'-As may be seen in Fig. 2c, the output of photocell 30 is in the form of rectangular pulses 44 of equal duration and time-spacing. These pulses operate the electronic switches 32 and 33 and are concurrent with the time intervals during which the desired pulse groups 40 and 41 occur. Hence, only the desired pulses 40 and 41 are supplied over leads 34 and 35 to pulse amplifier 36, to the exclusion of pulses 42 and 43.

Amplifier 36 is biased so that it passes'the pulses 40 only during the occurrence of control pulses 41. Thus, as shown in Fig. 2d, a selected number of pulses in each of groups 40 is derived in producing pulse groups 45. For example, in the group of pulses 4t), represented at the left side of Fig. 2a, there are six pulses which are supplied to amplifier 36. However, only three of'these pulses occur during the control pulse 41, shown at the left side of Fig. 21). As a result, but three pulses occur ingroup (left side of FigJZd) and are supplied to counter 37 as an indication of the instantaneous value t of'thepredetermined function. Theoutput of counter 37 is dependent upon the instantaneous number of pulses in each of groups 45, hence output device 38 indicates the instantaneous value of u. i r i ;It is thus evident that by employing two functions plotted on a common track in a selected alternating order,

possible.

a more compact arrangement is afforded than heretofore Moreover, since a single rotating member is employed for both the function-representing indicia and the interval-determining function, precise synchronism is maintained and the accuracy of computation is not undesirably impaired by variations in speed of the rotating member. 7

In addition, since a single disc is employed, it may be quickly and easily exchanged for another that carries a different function of independent variables.

Obviously, other types of synchronization apparatus may be employed in place of strips. 26-27 and photocell 30. For example, a generator of electrical impulses may be mechanically driven by motor 16 toprovide rectangular pulses 44 of Fig. 20. Alternatively, strip 26 may be constructed of an electrically conductive nia= terial and strip 27 may be an insulator. Thus, a pair of closely spaced brush-contacts connected in series with a battery may be arranged to engage strips 26-27 and provide synchronizing pulses.

Moreover, although electronic switches 32 and 33 have been illustrated in association with photocells 17 and 24 as the means for intercepting modulated light energy in accordance with the alternating order relationship of disc sections 11 and 22 so. that modulated energy may be selectively derived from each of curve groups 12 and 23, other arrangements may be employed.

For example, a circuit modification such as illustrated in Fig. 3 may be utilized to produce pulse output only during an interval of time wherein all of the light beams are interrupted. In Fig. 3, elements which have counterparts in Fig. 1 are represented by the same reference numeral followed by a prime designation.

Photocells 17, 24 and 30' are connected in parallel 1 and to the input circuit of a single-shot multivibrator 50.

By means of a bias source 51,.multivibrator 50 is adjusted so that it is operative to produce pulses of fixed amplitude and duration in response to pulses from photocell 17 solely in the presence of rectangular pulses from both photocells 24 and 39. Thus, corresponding pulses are supplied to counter 37 in response to those of pulses 40 (Fig. 2a) that are concurrent with both pulses 41 and 44 (Figs. 2b and c). 'Howfever, 'in the succeeding operating interval, pulse 42 does not render multivibrator 50 operative and it does not produce pulses in response to pulses 43. I

The plurality of photoelectric cells' illustrated in the system of Fig. 1 may be replaced by a single cell. Such a single photocell preferably is adapted to be completely saturated in the presence of any incident light. Accordingly, only the simultaneous occurrence of the interruption of all three beams provides an output pulse.

It may be appropriate to point out that light beam 15 preferably should have a cross-sectional dimension in the plane ofdisc 10 smaller than the width of curves 12. In this way, the incident light at photocell 17 may be completely interrupted and. thereby provide maximum pulse amplitude for reliable circuit operation. Of course, instead of disc 10 being transparent and the curve markings opaque, the disc may be opaque and the markings transparent. In the latter case, the cross-sectional dimension of beam 15 in the plane of the disc preferably should be smaller than the spacing between the closest of curves 12.

Also, disc 10, for example, may be divided into quadrants or any even-numbered equal intervals with functions of x and y alternately plotted thereon.

Still further, although a disc is preferred for com' 37. To relieve such a speed requirement, disc 10 may P6 provided with a peripheral track including equally same spaced markings. By 'm'e'ansof an additional photocell, associated with the track and "coupled to another ntegrator, a potential may be derived having an amplitude dependent upon the rotational 'speed of disc '10. This potential may be employed to control the output of an amplifier interposed between counter 37 and indicator 38 in such a manner as to correct for speed variations.

While particular embodiments of the present invention have been shown and described; it is apparent that changes and modifications, may be made without departing from this invention in its broader aspects, and therefore, the aim in the appended claims is to cover all such changes and modifications as fall within the true spirit and scope of this invention.

I claim:

1. Automatic computing apparatus comprising: a screen including first and second sections having indicia, said indicia of each of said sections representing a preselected function of at least one of a pair of independent variables in terms of a modifying effect on incident radiant energy, and said sections being distributed along a path in a predetermined alternating order; means for projecting radiant energy toward said screen in a pair of beams spaced along said path and individually positionable according to the instantaneous value of a respective one of said variables; means for relatively displacing said screen and said beams in a direction parallel to said .path to effect modulation of said beams; and means for intercepting radiant energy after said modulation and for deriving an output signal during operating intervals wherein said first section modulates one of said beams and said second section simultaneously modulates the other of said beams.

2. Automatic computing-apparatus comprising: means for deriving a pair of light beams individually positionable in response to the instantaneous value of a respective one of a pair of independent variables; a screen continuously displaced along a path intercepting. said pair of light beams in successive order and including first and second sections having indicia, said indicia of each of said sections representing a preselected function-of at least one of said variables in terms of a modifying eifect on incident light energy, and said sections being distributed along said path in a predetermined alternating order; and means for intercepting light energy after modification by said screen and for deriving an output signal during operating intervals wherein said first section simultaneously intercepts one of said light beams and said second section intercepts the other of said light beams to the exclusion of operating intervals wherein said first section intercepts said other beam and said second section intercepts said one beam.

3. Automatic computing apparatus comprising: a screen including a first section having a general background area and indicia defining a family of curves expressing a dependent variable 2 as a function of two independent variables x and y, and a second section having a general background area and other indicia dependent upon said variable y, said background areas and said indicia having different effects on incident radiant energy; means for displacing said screen to move said first and second screen sections in consecutive order along agiven path; means for projecting radiant energy toward said screen in first and second beams spaced from one another along said path; means for positioning each of said first and said second beams in a direction transverse to said path according to the instantaneousvalue of a respective one of said variables x and y;'means for interceptingsaid beams after modulation by said screen and for deriving corresponding first and second electrical signals; means operative synchronously with movement of said screen for deriving a time-divided portion of each of said first and said second signals representative solely of a respective one of said first and said second screen sections; means for utilizing said portion of said second signal "to establish a time interval for utilization of said'portion of'saidfirs't-signal; and means for indicating a characterincluding a first section-having a family of curves defining said function and a second section having a region defining a time interval dependent upon the speed of movement of said screen and the instantaneous value of one of said variables, said sections occurring in alternating order along said given path; means for projecting light energy toward said screen in first and second beams displaced relative to one another along said given path by an amount equal to the mean spacing between said first and said second sections of said screen; means for displacing said screen thereby to modulate each of said beams of light energy into pulsations representing said curves and said regions; means for positioning each of said beams transversely of said path in accordance with instantaneous values of a respective one of said independent variables; photoelectric means for intercepting said means after modulation thereby to derive electrical pulses corresponding to said pulsations of said light energy; electronic means responsive to said electrical pulses and operated synchronously with movement of said screen for deriving a pulse signal corresponding to a time-divided portion of the modulation of said first light beam by saidfirst section concurrent in time with the modulation of said second beam by said second section; and means for indicating the number of pulsations in said pulse signal thereby to represent the instantaneous value of said function. I V

5. Automatic computing apparatus for determining the value of a function of two independent variables comprising: a screen movable along a given path and including a first section having a family of curves defining said function and a second section having a region defining a time interval dependent upon the speed of movement of said screen and the instantaneous value of one of said variables, said sections occurring in alternating order along said given path, and said screen further including a synchronizing section having portions coeX- tensive with each of said first and said second sections; means for projecting light energy toward said screen in first and second beams displaced relative to one another along said given path by an amount equal to the mean spacing between said first and said second sections of said screen; means for displacingsaid screen thereby to modulate each of said beams of light energy into pulsations representing said curves andsaid regions; means for positioning each of said beams transversely of said path in accordance with instantaneous values of a respective one of said independent variables; photoelectric means for intercepting said beams after modulation thereby to derive electrical pulses corresponding to said pulsations of said light energy; means including a source of light energy and a photoelectric device cooperating with said synchronizing section for deriving synchronizing pulses; electronic means responsive to said electrical pulses and to said synchronizing pulses for deriving a pulse signal corresponding to a time-divided portion of the modulation of said first light beam by said first section concurrent in time with the modulation of said second beam by said second section; and means for indicating the number of'puls'ations in said pulse signal thereby to represent the instantaneous value'of ,said

function.

6. Automatic computing apparatus for determining the value of a function of twoindependent variables comprising; a screen movable along a given path and including a first section having a family of curves defining. said function and a second section having a region de- 7 fining a time interval dependent upon the speed of movement of said screen and the instantaneous value of one of said variables; said sections occurring in alternating order along said given'path; means for projecting light energy toward said screen in first and second beams dis- .placed relative to one another along said given path by an amount equal to the mean spacing between said first and said second sections of said screen; means for displacing said screen thereby to modulate each of said beams of light energy into pulsations representing said curves and said regions; means for positioning each of said beams transversely of saidpath in accordance with instantaneous values of a respective one of said independent variables; a pair of photocells each disposed to intercept one of said beams after modulation thereby to derive electrical pulses corresponding to said pulsations of said light energy; means for deriving synchronizing pulses representing movement of one of said sections relative to one of said beams; a pair of electronic switches,

each operated in response to said synchronizing pulses and coupled to said photocells for deriving respective signals corresponding to the modulation of one of said beams solely by one of said sections; means coupled to said electronic switches for deriving a pulse signal corresponding to a time-divided portion of the modulation of said first light beam by said first section concurrent in time with the modulation of said second beam by said second section; and means for indicating the number of pulsations in said pulse signal thereby to represent the instantaneous value of said function.

. 7. Automatic computing apparatus for determining the value of a function of two independent variables com prising: a screen movable along a given path and including a first section having a family of curves defining said function and a second section having a region defining a time interval dependent upon the speed of movement of said screen and the instantaneous value of one of said variables, said sections occurring in alternating order along said given path; means for projecting light energy toward said screen in first and second beams displaced relative to one another along said given path by an amount equal to the mean spacing between said first and said second sections of said screen; means for dis- .placing said screen thereby to modulate each of said beams of light energy into pulsations representing said curves and said regions; means for positioning each of said beams transversely of said path in accordance with instantaneous values of a respective one of said independent variables; photoelectric means for intercepting said beams after modulation thereby to derive two electrical pulse signals, each corresponding to said pulsations of said light energy in each of said beams; means for deriving synchronizing pulses representing movement of one of said sections relative to a corresponding one of said beams; a multivibrator conditioned to be inoperative except in the presence of three, coincident pulses supplied with said two electrical pulse signals and said synchronizing pulses for deriving a pulse signal corresponding to a time-divided portion of the modulation of said first light beam by said first section concurrent in time with the modulation of said second beam by said second section; and means for indicating the number of pulsations in said pulse signal thereby to represent the instantaneous value of said function.

8. A screen for displacement along a given path in association with an automatic computer comprising: a first section having a family of curves defining a function of two independent variables, and a second section disposed inalterna'ting relation with said first section along 'said given path and having a region defining a time in- 8 terval dependent upon the speed of movement of said screen and the instantaneous value of one of said variables.

9. A screen for displacement along a given path in association with an automatic computer comprising: a first section having a general background-area and indicia representing a family of curves defining a function of two independent variables and a second section disposed in alternating relation with said first section along said givenpath and having a general background area and indicia representing a region defining a time interval dependent upon the speed of movement of said screen and the instantaneous value of one of said variables, said general background areas and said indicia having different effects on incident radiant energy.

10. A screen for displacement along a given path in association with an automatic computer comprising: a first section having abgeneral background area and indicia representing a family of curves defining a function of two independent variables, a second section disposed in alternating relation with said first section along said given path and having a general 'background area and indicia representing a region defining a time interval dependent upon the speed of movement of said screen and the instantaneous value of one of said variables, said general background areas and said. indicia having different effects on incident radiant energy, and a third section including portions substantially coextensive with each of said first and said second sections, said portions having different effects on incident radiant energy.

11. A screen for rotation about a predetermined axis in association with an automatic computer comprising: a first section occupying a given segment of the disc defined by rotation of said screen about said axis and having a family of curves defining a function of two independent variables, and a second section occupying a segment of said disc other than said given segment and having a region defining a time interval dependent upon the speed of movement of said screen and the instantaneous value of one of said variables.

12. A screen for rotation about a predetermined axis in association with an automatic computer comprising: a first section occupying a given segment of the disc defined by rotation of said screen about said axis and having a general background area and indicia representing a family of curves defining a function of two independent variables, a second section occupying a segment of said disc other than said given segment and having a general background area and indicia representing a region defining a time interval dependent upon the speed of movement of said screen and the instantaneous value of one of said variables, said general background areas and said indicia having different effects on'incident radiant energy, and a third section disposed peripherally about said disc and including portions substantially coextensive with each of said first and said second sections, said portions having different effects on incident radiant energy.

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